Let L(x,y) represent x loves y
1. ∀x∀yL(x, y)) :Given predicate
Negation ¬∀x∀yL(x, y) = ∃x∃y¬L(x, y) : There is someone who doesn't love someone.Somebody hates somebody
2. ∀x∃y¬L(x, y) :Given predicate says everyone hates someone
Negation ¬∀x∃y¬L(x, y) =∃x∀yL(x, y) :- there is someone who loves everyone.
3.∃x∃yL(x, y)
Negation ∀x∀y¬L(x, y) : Everyone hates everyone. or nobody loves somebody
4.∀x∃yL(x, y)
Negation:- .∃x∀y¬L(x, y) : There is someone who hates everyone.Or somebody loves nobody